SOLUTION: How many liters of 15% acid and 33% acid should be mixed to make 40 liters of 21% acid solution ?

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Question 610624: How many liters of 15% acid and 33% acid should be mixed to make 40 liters of 21% acid solution ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 15% acid needed
Let +b+ = liters of 33% acid needed
+.15a+ = liters of acid in 15% solution
+.33b+ = liters of acid in 33% solution
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(1) +a+%2B+b+=+40+
(2) +%28+.15a+%2B+.33b+%29+%2F+40+=+.21+
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(2) +.15a+%2B+.33b+=+.21%2A40+
(2) +.15a+%2B+.33b+=+8.4+
(2) +15a+%2B+33b+=+840+
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Multiply both sides of (1) by +15+
and subtract (1) from (2)
(2) +15a+%2B+33b+=+840+
(1) +-15a+-+15b+=+600+
+18b+=+240+
+b+=+13.333+
and, since
(1) +a+%2B+13.333+=+40+
(1) +a+=+26.666+
26.667 liters of 15% acid are needed
13.333 liters of 33% acid are needed
check:
(2) +%28+.15a+%2B+.33b+%29+%2F+40+=+.21+
(2) +%28+.15%2A26.667+%2B+.33%2A13.333+%29+%2F+40+=+.21+
(2) +%28+4.000005+%2B+4.39989+%29+%2F+40+=+.21+
(2) +8.39994+%2F+40+=+.21+
(2) +8.39994+=+8.4+
Error must be due to rounding off